This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054850 #25 Aug 25 2024 09:49:39
%S A054850 1,2,4,7,11,14,18,23,27,32,37,42,48,53,59,64,70,76,82,88,95,101,107,
%T A054850 114,120,127,134,140,147,154,161,168,175,182,189,197,204,211,219,226,
%U A054850 234,241,249,256,264,272,279,287,295,303,311,318,326,334,342,350,358,367
%N A054850 Binary logarithm of n-th primorial, rounded down to an integer.
%C A054850 A measure of the growth rate of the primorials.
%H A054850 Michael De Vlieger, <a href="/A054850/b054850.txt">Table of n, a(n) for n = 1..10000</a>
%F A054850 a(n) = floor(log_2 n#) = m such that 2^m <= p(n)# < 2^(m + 1), where p(n)# is the primorial of the n-th prime (A002110).
%F A054850 a(n) = A000523(A002110(n)).
%F A054850 a(n) ~ n log n. - _Charles R Greathouse IV_, Aug 25 2024
%e A054850 The product of the first four primes is 2 * 3 * 5 * 7 = 210. In binary, 210 is 11010010, an 8-bit number, and we see that 2^7 < 210 < 2^8. And indeed log_2 210 = 7.7142455... and thus a(4) = 7.
%e A054850 a(5) = floor(log_2 2310) = floor(11.1736771363...) = 11.
%p A054850 a := n -> ilog2(mul(ithprime(i), i=1..n)):
%p A054850 seq(a(n), n=1..58); # _Peter Luschny_, Oct 18 2018
%t A054850 Table[Floor[Log[2, Product[Prime[i], {i, n}]]], {n, 60}]
%t A054850 Floor[Log2[#]]&/@FoldList[Times,Prime[Range[60]]] (* _Harvey P. Dale_, Aug 04 2021 *)
%o A054850 (PARI) a(n) = logint(prod(k=1, n, prime(k)), 2); \\ _Michel Marcus_, Jan 06 2020
%Y A054850 Cf. A000523, A002110, A058033.
%Y A054850 Equals A045716(n) - 1.
%K A054850 nonn
%O A054850 1,2
%A A054850 _Lekraj Beedassy_, May 22 2003
%E A054850 Edited, corrected and extended by _Robert G. Wilson v_, May 22 2003
%E A054850 Name simplified by _Alonso del Arte_, Oct 14 2018 (old name is now first formula).